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<h2>Similarity measures</h2>
<p>This is a short descriptions of the semantic similarity measures
  currently implemented in OntoSIML.</p>

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    <th>Jaccard:</th>
    <td>The similarity between an entity E1 with a set of annotations
    A1 and the entity E2 with a set of annotations A2 is defined
    by:
      \[
      jaccard(E1, E2) := \frac{|Cl(A1)\cap Cl(A2)|}{|Cl(A1) \cup Cl(A2)|}
      \]
      where Cl(X) is the <em>semantic closure</em> of a set of
    annotations (i.e., Cl(X) is the smallest set containing X and
    which is closed against the superclass relation).
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    <th>SimGIC:</th>
    <td>The simGIC similarity between an entity E1 with a set of
    annotations A1 and the entity E2 with a set of annotations A2 is
    defined by:
      \[
      simGIC(E1,E2) = \frac{\displaystyle\sum\limits_{x\in Cl(A1) \cap
      Cl(A2)}I(x)}{\displaystyle\sum\limits_{y\in Cl(A1) \cup Cl(A2)}I(y)}
      \]
      where I(x) is defined as
      \[
      I(x) = -\log(P(X=x))
      \]
      In other words, the simGIC measure is the jaccard measure
    weighted by the information content of an ontology class.
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    <th>Resnik's measure:</th>
    <td>Resnik's similarity measure between an entity E1 with a set of
    annotations A1 and the entity E2 with a set of annotations A2 is
    the information content of the most informative term in the
    intersection of A1 and A2. <em>Note that the results using
    this measure are not normalized to the [0,1] interval</em>.
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